fmm3dbie-webgpu-poc

A point source at a fixed frequency in a closed room with partially absorbing walls, solved with a high-order boundary integral equation on your GPU through WebGPU, in single precision. This is a browser port of a CUDA proof of concept for fmm3dbie's interior Helmholtz impedance solver. Choose the problem, press Solve, then turn the room with the mouse and click a slice to move the source.

case wavenumber k wall admittance β patches per face edge m order per patch room shape exponent p source (x, y, z) GMRES tolerance slice resolution

self-test

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show animate over one period walls xy xz yz

Press Solve to compute the field.

drag to turn · scroll to zoom · the nearer walls are cut away

no solve yet

What is computed

The room is the superellipsoid |x|^p + |y|^p + |z|^p = 1, with a point source inside and impedance walls (∂u/∂n − ikβu = 0). We solve fmm3dbie's combined field integral equation on 6m² curved patches: near interactions use precomputed quadrature weights, far interactions a direct sum, and GMRES runs on the CPU. The GPU work is in single precision.

The self-test solves a problem with a known solution and reports the error. The energy mismatch compares the power from the source with the power absorbed by the walls. Large cases may need more GPU memory than the browser allows.